It is well known that MIMO systems can provide high spectral efficiency compared to single input single output (SISO) systems for wireless communications. The MIMO system is considered one of the principal technologies for the next generation mobile communication because no additional bandwidth or transmit power is required to increase the capacity of the system. As in the case of SISO systems, several decoding schemes have been considered in many studies for the decoding of MIMO systems. Among the decoding schemes for MIMO systems, the maximum likelihood (ML) decoder provides the optimal bit error rate (BER) performance at the expense of quite severe computational requirement.
The sphere decoder (SD) has been introduced as an interesting means to reduce the excessive computational complexity of the conventional full-search ML decoder. The breadth-first signal decoder (BSIDE) has recently been proposed and shown to have lower computational complexity than the SD in general. Despite various studies for designing ML decoders with a reduced computational complexity, however, the computational complexity of the ML decoders is still somewhat higher than that of practical systems.
In a number of studies, several near ML decoders with a reasonable loss in the BER performance have been proposed to achieve lower computational complexity for the decoding of MIMO systems. Most of the near ML decoders perform QR decomposition (QRD) of the channel matrix and regard the decoding problem as a problem of searching for a lattice point with the smallest node metric by employing the depth-, breadth-, or metric-first search method on a tree.
Among a variety of near ML decoders, Schnorr-Euchner2 (SE2) scheme and increasing radii algorithm (IRA) have been proposed to alleviate the exponentially growing computational complexity of the depth-first search when the number of layers increases. As variants of the SD, the SE2 and IRA both employ unique methods for the determination of the threshold and repeat searching the tree back and forth to find a node with the smallest metric. The SE2 scheme reduces the computational complexity based on Schnorr-Euchner (SE) enumeration with a Fano-like metric bias and an early termination technique. On the other hand, the IRA reduces the computational complexity by pruning the search space statistically, offering substantial computational savings when the number of antennas is large. Although the SE2 and IRA both achieve near ML performance with low computational complexity, the SE2 requires an estimate of the signal to noise ratio (SNR) and the IRA is required to restart the search from the beginning with an increased radius when no feasible point is found.
As for the decoding schemes based on the breadth-first search method, the QRD-M scheme is based on the classical M-algorithm and exhibits quite a low computational complexity, searching the tree only in the ‘forward’ direction from the root of a tree. In order to prevent a full search of the tree, the QRD-M retains only M nodes with the smallest node metric in each layer. The adaptive QRD-M and efficient QRD-M schemes have also been proposed to further reduce the computational complexity of the QRD-M. The efficient QRD-M achieves a reduction in the computational complexity by discarding a node when the node metric is larger than a threshold: however, the partial decision feedback equalizer (DFE) solution and the Euclidean distance of the DFE solution need to be computed in each layer.
Based on the metric-first search, the QRD-Stack scheme relies on the stack algorithm and searches branches extended from a node with the smallest node metric. Although the QRD-Stack allows a low computational complexity by retaining only a few nodes for search, backtracking is quite frequent at low SNR since a number of nodes, not necessarily in the same layer, are considered simultaneously.